When controlling a linear motion stage, oscillatory motions inherently occur, resulting in unstable operations and undesirable oscillation responses.
Therefore, an analysis of the frequency response generally is performed to determine the type, frequency, and amplitude of the oscillation, according to which a suitable filter is designed in order to eliminate the inherent oscillatory motions of the linear motion stage, thus stabilizing it and improving the capability of the controlling response. The filter generally is designed to have a single cut-off frequency regardless of the positions of the linear motion stage.
However, the inherent oscillation of the linear motion stage varies with the driven positions of the linear motion stage according to the type and structure of the linear motion stage. For example, the inherent oscillation frequency of the linear motion stage varies with the position of the slide according to working/assembling/frictional characteristics for a single axial stage, and additionally with the position of the slide along both axes for an X-Y stage.
FIGS. 1(a) and 1(b) illustrate an example of the resonance frequency varying with the position of a linear motion stage. FIG. 1(a) illustrates the frequency response of the Y-axis at X and Y coordinates (0 mm, 0 mm) in a stacked X-Y stage, and FIG. 1(b) illustrates the frequency response of the Y-axis at X and Y coordinates (225 mm, 300 mm) in a stacked X-Y stage.
In case the degree of the linear motion stage's assembling or working deviates greatly according to its driven positions, or in case of a linear motion stage with two or more axes connected to each other, the inherent oscillation frequency and amplitude vary with the driven position of the stage, as shown in FIGS. 1 (a) and 1(b). Thus, in conventional system employing a filter having a single representative cut-off frequency, the filter cannot properly perform its function over the whole operational range of the linear motion stage, and accordingly in some cases there occurs an unstable frequency amplified to make the linear motion system unstable, for which the filter cannot be applied.
FIGS. 2(a) and 2(b) illustrate an example of controlling response by a resonance frequency varying with the position of the linear motion stage. FIG. 2(a) illustrates the control response of the Y-axis at X and Y coordinates (0 mm, 0 mm) in a stacked X-Y stage, and FIG. 2(b) illustrates the control response of the Y-axis at X and Y coordinates (225 mm, 300 mm) in a stacked X-Y stage.
In case the inherent oscillation frequency and amplitude vary with the driven position of the stage, as illustrated in
FIGS. 1(a) and 1(b), a filter with a fixed cut-off frequency and fixed amplitude cannot properly perform its filtering function over the whole operational range of the stage, resulting in the control response mixed with oscillation components, as illustrated in FIGS. 2(a) and 2(b).